Regina Calculation Engine
Public Member Functions | Static Public Member Functions
regina::NLayeredSolidTorus Class Reference

Represents a layered solid torus in a triangulation. More...

#include <subcomplex/nlayeredsolidtorus.h>

Inheritance diagram for regina::NLayeredSolidTorus:
regina::NStandardTriangulation regina::ShareableObject regina::boost::noncopyable

List of all members.

Public Member Functions

NLayeredSolidTorusclone () const
 Returns a newly created clone of this structure.
unsigned long getNumberOfTetrahedra () const
 Returns the number of tetrahedra in this layered solid torus.
NTetrahedrongetBase () const
 Returns the tetrahedron that is glued to itself at the base of this layered solid torus.
int getBaseEdge (int group, int index) const
 Returns the requested edge of the base tetrahedron belonging to the given group.
int getBaseEdgeGroup (int edge) const
 Returns the group that the given edge of the base tetrahedron belongs to.
int getBaseFace (int index) const
 Returns one of the two faces of the base tetrahedron that are glued to each other.
NTetrahedrongetTopLevel () const
 Returns the top level tetrahedron in this layered solid torus.
unsigned long getMeridinalCuts (int group) const
 Returns the number of times the meridinal disc of the torus cuts the top level tetrahedron edges in the given group.
int getTopEdge (int group, int index) const
 Returns the requested edge of the top level tetrahedron belonging to the given group.
int getTopEdgeGroup (int edge) const
 Returns the group that the given edge of the top level tetrahedron belongs to.
int getTopFace (int index) const
 Returns one of the two faces of the top level tetrahedron that form the boundary of this layered solid torus.
NTriangulationflatten (const NTriangulation *original, int mobiusBandBdry) const
 Flattens this layered solid torus to a Mobius band.
void transform (const NTriangulation *originalTri, const NIsomorphism *iso, NTriangulation *newTri)
 Adjusts the details of this layered solid torus according to the given isomorphism between triangulations.
NManifoldgetManifold () const
 Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented.
NAbelianGroupgetHomologyH1 () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented.
std::ostream & writeName (std::ostream &out) const
 Writes the name of this triangulation as a human-readable string to the given output stream.
std::ostream & writeTeXName (std::ostream &out) const
 Writes the name of this triangulation in TeX format to the given output stream.
void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream.
- Public Member Functions inherited from regina::NStandardTriangulation
virtual ~NStandardTriangulation ()
 A destructor that does nothing.
std::string getName () const
 Returns the name of this specific triangulation as a human-readable string.
std::string getTeXName () const
 Returns the name of this specific triangulation in TeX format.
virtual void writeTextShort (std::ostream &out) const
 Writes this object in short text format to the given output stream.
- Public Member Functions inherited from regina::ShareableObject
 ShareableObject ()
 Default constructor that does nothing.
virtual ~ShareableObject ()
 Default destructor that does nothing.
std::string toString () const
 Returns the output from writeTextShort() as a string.
std::string toStringLong () const
 Returns the output from writeTextLong() as a string.

Static Public Member Functions

static NLayeredSolidTorusformsLayeredSolidTorusBase (NTetrahedron *tet)
 Determines if the given tetrahedron forms the base of a layered solid torus within a triangulation.
static NLayeredSolidTorusformsLayeredSolidTorusTop (NTetrahedron *tet, unsigned topFace1, unsigned topFace2)
 Determines if the given tetrahedron forms the top level tetrahedron of a layered solid torus, with the two given faces of this tetrahedron representing the boundary of the layered solid torus.
static NLayeredSolidTorusisLayeredSolidTorus (NComponent *comp)
 Determines if the given triangulation component forms a layered solid torus in its entirity.
- Static Public Member Functions inherited from regina::NStandardTriangulation
static NStandardTriangulationisStandardTriangulation (NComponent *component)
 Determines whether the given component represents one of the standard triangulations understood by Regina.
static NStandardTriangulationisStandardTriangulation (NTriangulation *tri)
 Determines whether the given triangulation represents one of the standard triangulations understood by Regina.

Detailed Description

Represents a layered solid torus in a triangulation.

A layered solid torus must contain at least one tetrahedron.

Note that this class only represents layered solid tori with a (3,2,1) at their base. Thus triangulations that begin with a degenerate (2,1,1) mobius strip and layer over the mobius strip boundary (including the minimal (1,1,0) triangulation) are not described by this class.

All optional NStandardTriangulation routines are implemented for this class.


Member Function Documentation

NLayeredSolidTorus* regina::NLayeredSolidTorus::clone ( ) const

Returns a newly created clone of this structure.

Returns:
a newly created clone.
NTriangulation* regina::NLayeredSolidTorus::flatten ( const NTriangulation original,
int  mobiusBandBdry 
) const

Flattens this layered solid torus to a Mobius band.

A newly created modified triangulation is returned; the original triangulation is unchanged.

Note that there are three different ways in which this layered solid torus can be flattened, corresponding to the three different edges of the boundary torus that could become the boundary edge of the new Mobius band.

Parameters:
originalthe triangulation containing this layered solid torus; this triangulation will not be changed.
mobiusBandBdrythe edge group on the boundary of this layered solid torus that will become the boundary of the new Mobius band (the remaining edge groups will become internal edges of the new Mobius band). This must be 0, 1 or 2. See getTopEdge() for further details about edge groups.
Returns:
a newly created triangulation in which this layered solid torus has been flattened to a Mobius band.
static NLayeredSolidTorus* regina::NLayeredSolidTorus::formsLayeredSolidTorusBase ( NTetrahedron tet)
static

Determines if the given tetrahedron forms the base of a layered solid torus within a triangulation.

The torus need not be the entire triangulation; the top level tetrahedron of the torus may be glued to something else (or to itself).

Note that the base tetrahedron of a layered solid torus is the tetrahedron furthest from the boundary of the torus, i.e. the tetrahedron glued to itself with a twist.

Parameters:
tetthe tetrahedron to examine as a potential base.
Returns:
a newly created structure containing details of the layered solid torus, or null if the given tetrahedron is not the base of a layered solid torus.
static NLayeredSolidTorus* regina::NLayeredSolidTorus::formsLayeredSolidTorusTop ( NTetrahedron tet,
unsigned  topFace1,
unsigned  topFace2 
)
static

Determines if the given tetrahedron forms the top level tetrahedron of a layered solid torus, with the two given faces of this tetrahedron representing the boundary of the layered solid torus.

Note that the two given faces need not be boundary faces in the overall triangulation. That is, the layered solid torus may be a subcomplex of some larger triangulation. For example, the two given faces may be joined to some other tetrahedra outside the layered solid torus or they may be joined to each other. In fact, they may even extend this smaller layered solid torus to a larger layered solid torus.

Parameters:
tetthe tetrahedron to examine as a potential top level of a layered solid torus.
topFace1the face number of the given tetrahedron that should represent the first boundary face of the layered solid torus. This should be between 0 and 3 inclusive.
topFace2the face number of the given tetrahedron that should represent the second boundary face of the layered solid torus. This should be between 0 and 3 inclusive, and should not be equal to topFace1.
Returns:
a newly created structure containing details of the layered solid torus, or null if the given tetrahedron with its two faces do not form the top level of a layered solid torus.
NTetrahedron * regina::NLayeredSolidTorus::getBase ( ) const
inline

Returns the tetrahedron that is glued to itself at the base of this layered solid torus.

Returns:
the base tetrahedron.
int regina::NLayeredSolidTorus::getBaseEdge ( int  group,
int  index 
) const
inline

Returns the requested edge of the base tetrahedron belonging to the given group.

The layering identifies the six edges of the base tetrahedron into a group of three, a group of two and a single unidentified edge; these are referred to as groups 3, 2 and 1 respectively.

Note that getBaseEdgeGroup(getBaseEdge(group, index)) == group for all values of group and index.

Edges getBaseEdge(2,0) and getBaseEdge(3,0) will both belong to face getBaseFace(0). Edges getBaseEdge(2,1) and getBaseEdge(3,2) will both belong to face getBaseFace(1).

Parameters:
groupthe group that the requested edge should belong to; this must be 1, 2 or 3.
indexthe index within the given group of the requested edge; this must be between 0 and group-1 inclusive. Note that in group 3 the edge at index 1 is adjacent to both the edges at indexes 0 and 2.
Returns:
the edge number in the base tetrahedron of the requested edge; this will be between 0 and 5 inclusive.
int regina::NLayeredSolidTorus::getBaseEdgeGroup ( int  edge) const
inline

Returns the group that the given edge of the base tetrahedron belongs to.

See getBaseEdge() for further details about groups.

Note that getBaseEdgeGroup(getBaseEdge(group, index)) == group for all values of group and index.

Parameters:
edgethe edge number in the base tetrahedron of the given edge; this must be between 0 and 5 inclusive.
Returns:
the group to which the given edge belongs; this will be 1, 2 or 3.
int regina::NLayeredSolidTorus::getBaseFace ( int  index) const
inline

Returns one of the two faces of the base tetrahedron that are glued to each other.

Parameters:
indexspecifies which of the two faces to return; this must be 0 or 1.
Returns:
the requested face number in the base tetrahedron; this will be between 0 and 3 inclusive.
NAbelianGroup* regina::NLayeredSolidTorus::getHomologyH1 ( ) const
virtual

Returns the expected first homology group of this triangulation, if such a routine has been implemented.

If the calculation of homology has not yet been implemented for this triangulation then this routine will return 0.

This routine does not work by calling NTriangulation::getHomologyH1() on the associated real triangulation. Instead the homology is calculated directly from the known properties of this standard triangulation.

The details of which standard triangulations have homology calculation routines can be found in the notes for the corresponding subclasses of NStandardTriangulation. The default implementation of this routine returns 0.

The homology group will be newly allocated and must be destroyed by the caller of this routine.

If this NStandardTriangulation describes an entire NTriangulation (and not just a part thereof) then the results of this routine should be identical to the homology group obtained by calling NTriangulation::getHomologyH1() upon the associated real triangulation.

Returns:
the first homology group of this triangulation, or 0 if the appropriate calculation routine has not yet been implemented.

Reimplemented from regina::NStandardTriangulation.

NManifold* regina::NLayeredSolidTorus::getManifold ( ) const
virtual

Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented.

If the 3-manifold cannot be recognised then this routine will return 0.

The details of which standard triangulations have 3-manifold recognition routines can be found in the notes for the corresponding subclasses of NStandardTriangulation. The default implementation of this routine returns 0.

It is expected that the number of triangulations whose underlying 3-manifolds can be recognised will grow between releases.

The 3-manifold will be newly allocated and must be destroyed by the caller of this routine.

Returns:
the underlying 3-manifold.

Reimplemented from regina::NStandardTriangulation.

unsigned long regina::NLayeredSolidTorus::getMeridinalCuts ( int  group) const
inline

Returns the number of times the meridinal disc of the torus cuts the top level tetrahedron edges in the given group.

See getTopEdge() for further details about groups.

Parameters:
groupthe given edge group; this must be 0, 1 or 2.
Returns:
the number of times the meridinal disc cuts the edges in the given group.
unsigned long regina::NLayeredSolidTorus::getNumberOfTetrahedra ( ) const
inline

Returns the number of tetrahedra in this layered solid torus.

Returns:
the number of tetrahedra.
int regina::NLayeredSolidTorus::getTopEdge ( int  group,
int  index 
) const
inline

Returns the requested edge of the top level tetrahedron belonging to the given group.

The layering reduces five of the top level tetrahedron edges to three boundary edges of the solid torus; this divides the five initial edges into groups of size two, two and one.

Group 0 represents the boundary edge that the meridinal disc cuts fewest times. Group 2 represents the boundary edge that the meridinal disc cuts most times. Group 1 is in the middle.

Note that getTopEdgeGroup(getTopEdge(group, index)) == group for all values of group and index that actually correspond to an edge.

Edges getTopEdge(group, 0) will all belong to face getTopFace(0). Edges getTopEdge(group, 1) (if they exist) will all belong to face getTopFace(1).

Parameters:
groupthe group that the requested edge should belong to; this must be 0, 1 or 2.
indexthe index within the given group of the requested edge; this must be 0 or 1. Note that one of the groups only contains one tetrahedron edge, in which case this edge will be stored at index 0.
Returns:
the edge number in the top level tetrahedron of the requested edge (between 0 and 5 inclusive), or -1 if there is no such edge (only possible if the given group was the group of size one and the given index was 1).
int regina::NLayeredSolidTorus::getTopEdgeGroup ( int  edge) const
inline

Returns the group that the given edge of the top level tetrahedron belongs to.

See getTopEdge() for further details about groups.

Note that getTopEdgeGroup(getTopEdge(group, index)) == group for all values of group and index that actually correspond to an edge.

Parameters:
edgethe edge number in the top level tetrahedron of the given edge; this must be between 0 and 5 inclusive.
Returns:
the group to which the given edge belongs (0, 1 or 2), or -1 if this edge does not belong to any group (only possible if this is the unique edge in the top tetrahedron not on the torus boundary).
int regina::NLayeredSolidTorus::getTopFace ( int  index) const
inline

Returns one of the two faces of the top level tetrahedron that form the boundary of this layered solid torus.

Parameters:
indexspecifies which of the two faces to return; this must be 0 or 1.
Returns:
the requested face number in the top level tetrahedron; this will be between 0 and 3 inclusive.
NTetrahedron * regina::NLayeredSolidTorus::getTopLevel ( ) const
inline

Returns the top level tetrahedron in this layered solid torus.

This is the tetrahedron that would be on the boundary of the torus if the torus were the entire manifold.

Returns:
the top level tetrahedron.
static NLayeredSolidTorus* regina::NLayeredSolidTorus::isLayeredSolidTorus ( NComponent comp)
static

Determines if the given triangulation component forms a layered solid torus in its entirity.

Note that, unlike formsLayeredSolidTorusBase(), this routine tests for a component that is a layered solid torus with no additional tetrahedra or gluings. That is, the two boundary faces of the layered solid torus must in fact be boundary faces of the component.

Parameters:
compthe triangulation component to examine.
Returns:
a newly created structure containing details of the layered solid torus, or null if the given component is not a layered solid torus.
void regina::NLayeredSolidTorus::transform ( const NTriangulation originalTri,
const NIsomorphism iso,
NTriangulation newTri 
)

Adjusts the details of this layered solid torus according to the given isomorphism between triangulations.

The given isomorphism must describe a mapping from originalTri to newTri, and this layered solid torus must currently refer to tetrahedra in originalTri. After this routine is called this structure will instead refer to the corresponding tetrahedra in newTri (with changes in vertex/face numbering also accounted for).

Precondition:
This layered solid torus currently refers to tetrahedra in originalTri, and iso describes a mapping from originalTri to newTri.
Parameters:
originalTrithe triangulation currently referenced by this layered solid torus.
isothe mapping from originalTri to newTri.
newTrithe triangulation to be referenced by the updated layered solid torus.
std::ostream & regina::NLayeredSolidTorus::writeName ( std::ostream &  out) const
inlinevirtual

Writes the name of this triangulation as a human-readable string to the given output stream.

Python:
The parameter out does not exist; standard output will be used.
Parameters:
outthe output stream to which to write.
Returns:
a reference to the given output stream.

Implements regina::NStandardTriangulation.

std::ostream & regina::NLayeredSolidTorus::writeTeXName ( std::ostream &  out) const
inlinevirtual

Writes the name of this triangulation in TeX format to the given output stream.

No leading or trailing dollar signs will be included.

Warning:
The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.
Python:
The parameter out does not exist; standard output will be used.
Parameters:
outthe output stream to which to write.
Returns:
a reference to the given output stream.

Implements regina::NStandardTriangulation.

void regina::NLayeredSolidTorus::writeTextLong ( std::ostream &  out) const
inlinevirtual

Writes this object in long text format to the given output stream.

The output should provided the user with all the information they could want. The output should end with a newline.

The default implementation of this routine merely calls writeTextShort() and adds a newline.

Python:
The parameter out does not exist; standard output will be used.
Parameters:
outthe output stream to which to write.

Reimplemented from regina::ShareableObject.


The documentation for this class was generated from the following file:

Copyright © 1999-2012, The Regina development team
This software is released under the GNU General Public License.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).